What number should be added to both sides of the equation to complete the square (x² – 6x = 5)?
Answer: The number 9 should be added to both sides to complete the square.
Completing the Square
Completing the square is a technique used in algebra to solve quadratic equations. The method involves converting the quadratic equation into a perfect square trinomial by adding a specific value to both sides. For the equation x² – 6x = 5, we take half of the coefficient of x, which is -6/2 = -3, and square it, giving us 9. Adding 9 to both sides gives us x² – 6x + 9 = 14, which can be written as (x – 3)² = 14. This method is not just a mathematical trick; it’s a fundamental concept that helps in understanding the nature of quadratic equations and is widely used in various branches of mathematics, physics, and engineering.
FAQ on Completing the Square
How do you solve a quadratic equation by factoring?
Set the equation to zero, find factors of the quadratic, and solve for the variable.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² – 4ac)) / (2a).
What is the discriminant in a quadratic equation?
The discriminant is b² – 4ac and determines the nature of the roots.
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